# Acid-base Equilibria

> Edexcel International A-Level Chemistry · IAL Chemistry U4
> Source: https://www.owlsprep.com/study/edexcel-ial-chemistry-u4-acid-base-equilibria/

This guide covers all Edexcel IAL Chemistry Unit 4 acid-base equilibria content, from Brønsted-Lowry definitions and pH calculations to titration curves, buffer systems, and Core Practical 11 for Ka determination.

**Prerequisites:** [Basic acid-base reaction and molar titration calculations from Unit 2](https://www.owlsprep.com/study//edexcel-ial-chemistry-u2-acid-base-titrations/); [Equilibrium constant principles from Unit 4 Topic 13](https://www.owlsprep.com/study//edexcel-ial-chemistry-u4-equilibrium-constants/)

## Learning objectives

- Define Brønsted-Lowry acids, bases and conjugate acid-base pairs
- Calculate pH of strong/weak acids and strong bases using Ka, Kw and pKa values with allowed approximations
- Interpret titration curves for all strong/weak monoprotic and diprotic combinations
- Select appropriate indicators for titrations using curve data and indicator ranges
- Explain buffer action, calculate buffer pH, and describe the biological blood buffer system
- Determine Ka from experimental pH data and half-neutralisation points on titration curves
- Carry out Core Practical 11 for the determination of the Ka of a weak acid

## Fundamental Acid-Base Definitions and Strong Acid pH Calculations

**Brønsted-Lowry Acid-Base Pair** — An acid is a proton (H⁺) donor, while a base is a proton acceptor. A conjugate pair consists of two species that differ by exactly one H⁺ ion: the conjugate base is the species left after an acid donates a proton, and the conjugate acid is the species formed when a base accepts a proton.

*Example:* Hydrochloric acid (HCl, acid) donates H⁺ to form its conjugate base Cl⁻; ammonia (NH₃, base) accepts H⁺ to form its conjugate acid NH₄⁺.

Acid strength is determined by **degree of dissociation**, not concentration: strong acids dissociate 100% in aqueous solution, while weak acids only dissociate partially. pH is a logarithmic measure of hydrogen ion concentration, always reported to 2 decimal places in Edexcel exams.

$$pH = -\text{log}_{10}[H^+] \\ [H^+] = 10^{-pH}$$

**Worked example:** Calculate the pH of 0.005 mol dm⁻³ nitric acid (strong monoprotic acid) at 298K.

1. Strong monoprotic acids dissociate completely, so $[H^+] = $ initial acid concentration = 0.005 mol dm⁻³.
2. $$pH = -\text{log}_{10}(0.005) = 2.30$$

## Ka, Kw and pH Calculations for Weak Acids & Strong Bases

**Acid Dissociation Constant (Ka)** — Equilibrium constant for the partial dissociation of a weak acid HA: $HA \rightleftharpoons H^+ + A^-$. The expression is: $K_a = \frac{[H^+][A^-]}{[HA]}$. $pK_a = -log_{10}K_a$, so smaller pKa values correspond to stronger weak acids.

*Notation:* K_a

**Ionic Product of Water (Kw)** — Equilibrium constant for the dissociation of water: $H_2O \rightleftharpoons H^+ + OH^-$. At 298K, $K_w = [H^+][OH^-] = 1.0 × 10^{-14} mol^2 dm^{-6}$, so $pK_w = 14$.

*Notation:* K_w

> **Approximations for Weak Acid pH**
>
> No quadratic solving is required for Edexcel exams: use two valid approximations: 1) $[H^+] ≈ [A^-]$ (ignore H⁺ from water dissociation), 2) $[HA] ≈ $ initial acid concentration (ignore tiny amount of HA that dissociates). This simplifies the Ka expression to $[H^+] = \sqrt{K_a \times c}$.

**Worked example:** Calculate the pH of 0.02 mol dm⁻³ propanoic acid, given $K_a = 1.35 × 10^{-5} mol dm^{-3}$ at 298K.

1. Apply allowed approximations to find $[H^+]$:
2. $$[H^+] = \sqrt{1.35 × 10^{-5} × 0.02} = \sqrt{2.7 × 10^{-7}} = 5.196 × 10^{-4} mol dm^{-3}$$
3. Calculate pH to 2 decimal places:
4. $$pH = -\text{log}_{10}(5.196 × 10^{-4}) = 3.28$$

**Worked example:** Calculate the pH of 0.01 mol dm⁻³ barium hydroxide (strong dibasic base) at 298K.

1. Barium hydroxide dissociates completely: $Ba(OH)_2 → Ba^{2+} + 2OH^-$, so $[OH^-] = 2 × 0.01 = 0.02 mol dm^{-3}$.
2. Use Kw to find $[H^+]$:
3. $$[H^+] = \frac{K_w}{[OH^-]} = \frac{1.0 × 10^{-14}}{0.02} = 5.0 × 10^{-13} mol dm^{-3}$$
4. $$pH = -\text{log}_{10}(5.0 × 10^{-13}) = 12.30$$

## Titration Curves and Indicator Selection

Titration curves plot pH against volume of titrant added. Key features include: initial pH, a vertical section (rapid pH change near the equivalence point), equivalence point, and (for weak acid/strong base titrations) the half-neutralisation point. Diprotic acids have two separate vertical sections, one for each dissociable proton.

> **Indicator Selection Rule**
>
> To select a suitable indicator, its full pH range (given in the data booklet) must lie *entirely within* the vertical section of the titration curve. Common indicators are methyl orange (range 3.1–4.4) and phenolphthalein (range 8.3–10.0).

**Worked example:** A titration of ammonia (weak base) with hydrochloric acid (strong acid) has a vertical section from pH 3 to pH 7. State the suitable indicator for this titration.

1. Check indicator ranges against the vertical section:
2. Phenolphthalein (8.3–10.0) falls completely outside the vertical section, so is unsuitable.
3. Methyl orange (3.1–4.4) falls entirely inside the vertical section, so is the correct indicator.

## Buffer Systems and Calculations

**Buffer Solution** — A solution that resists changes in pH when small amounts of acid, base, or water are added. Acid buffers are made from a weak acid and its conjugate base (e.g. ethanoic acid + sodium ethanoate), while alkaline buffers are made from a weak base and its conjugate acid.

*Example:* Human blood uses an acid buffer system of carbonic acid ($H_2CO_3$) and hydrogencarbonate ions ($HCO_3^-$) to maintain a constant pH of ~7.4.

Buffer action works by reacting added H⁺ or OH⁻ with buffer components: added H⁺ reacts with the conjugate base ($H^+ + A^- → HA$), while added OH⁻ reacts with the weak acid ($OH^- + HA → A^- + H_2O$). The rearranged Ka expression is used to calculate buffer pH: $[H^+] = K_a × \frac{[HA]}{[A^-]}$.

**Worked example:** A buffer is made by mixing equal volumes of 0.1 mol dm⁻³ ethanoic acid and 0.05 mol dm⁻³ sodium ethanoate. Given $K_a = 1.7 × 10^{-5} mol dm^{-3}$, calculate the buffer pH.

1. Equal volumes halve both concentrations: $[HA] = 0.05 mol dm^{-3}$, $[A^-] = 0.025 mol dm^{-3}$.
2. Substitute into the buffer pH formula:
3. $$[H^+] = 1.7 × 10^{-5} × \frac{0.05}{0.025} = 3.4 × 10^{-5} mol dm^{-3}$$
4. $$pH = -\text{log}_{10}(3.4 × 10^{-5}) = 4.47$$

## Experimental Ka Determination (Core Practical 11)

There are two approved methods to determine the Ka of a weak acid for Core Practical 11: 1) Measure the pH of a known concentration of weak acid, then rearrange the Ka expression to calculate Ka. 2) Titrate the weak acid against a standard strong base, read the pH at the half-neutralisation point, where $pH = pK_a$ so $K_a = 10^{-pH}$.

**Worked example:** 25 cm³ of 0.1 mol dm⁻³ methanoic acid is titrated against 0.1 mol dm⁻³ NaOH. The pH at 12.5 cm³ of NaOH added is 3.75. Calculate the Ka of methanoic acid.

1. 12.5 cm³ is exactly half the volume required to reach equivalence, so this is the half-neutralisation point.
2. At half-neutralisation, $pH = pK_a = 3.75$.
3. $$K_a = 10^{-3.75} = 1.8 × 10^{-4} mol dm^{-3}$$

## Common pitfalls

- **Wrong:** Confusing acid strength (strong/weak) with concentration (concentrated/dilute)
  - Why it fails: Strength refers only to degree of dissociation, not concentration: a dilute strong acid can have a higher pH than a concentrated weak acid.
  - Correct: Classify acid strength using degree of dissociation, and use concentration only for pH calculations.
- **Wrong:** Attempting to solve quadratic equations for weak acid pH
  - Why it fails: Edexcel explicitly allows valid approximations for IAL Chemistry Unit 4, so quadratics are unnecessary and waste exam time.
  - Correct: Use $[H^+] = \sqrt{K_a × c}$ with the assumptions that $[HA] ≈ $ initial concentration and $[H^+] ≈ [A^-]$.
- **Wrong:** Assuming all titrations have an equivalence point at pH 7
  - Why it fails: Only strong acid + strong base titrations have equivalence at pH 7. Weak acid + strong base = pH >7, strong acid + weak base = pH <7.
  - Correct: Predict equivalence pH based on the relative strength of the acid and base used in the titration.
- **Wrong:** Selecting an indicator with a range that only partially overlaps the titration curve vertical section
  - Why it fails: The indicator will change colour gradually outside the equivalence point, leading to inaccurate titre values.
  - Correct: Only select indicators whose full pH range lies entirely within the vertical section of the titration curve.
- **Wrong:** Forgetting diprotic acids have two equivalence points on titration curves
  - Why it fails: Each proton in a diprotic acid dissociates separately, leading to two distinct vertical sections on the curve.
  - Correct: Count vertical sections to distinguish monoprotic and diprotic acids, and use the first half-neutralisation point to calculate Ka₁.
- **Wrong:** Reporting pH values to 1 or 0 decimal places
  - Why it fails: Edexcel mark schemes explicitly require pH values to be reported to 2 decimal places for all calculations.
  - Correct: Always round pH to 2 decimal places, even for whole number values (e.g. pH 2 is written as 2.00).

## Cheatsheet

| Concept | Formula/Rule | Exam Notes |
| --- | --- | --- |
| pH definition | $pH = -log_{10}[H^+]$; $[H^+] = 10^{-pH}$ | Report pH to 2 decimal places |
| Strong acid pH | $[H^+] = $ initial monoprotic acid concentration | Complete dissociation, no approximations needed |
| Weak acid pH | $[H^+] = \sqrt{K_a × c}$ | Approximations allowed, no quadratics required |
| Strong base pH | $[H^+] = \frac{K_w}{[OH^-]}$ | $K_w = 1.0×10^{-14} mol^2 dm^{-6}$ at 298K |
| Buffer pH | $[H^+] = K_a × \frac{[HA]}{[A^-]}$ | Assume no dissociation of buffer components |
| Half-neutralisation | $pH = pK_a$ | Only for weak acid + strong base titrations |
| Indicator selection | Full indicator range inside curve vertical section | Ranges provided in data booklet |

## What's next

Acid-base equilibria accounts for ~15% of the Edexcel IAL Chemistry Unit 4 written paper, so practice past paper questions on pH calculations, titration curve interpretation and buffer problems to consolidate your knowledge. Make sure you are fully confident with Core Practical 11, as practical-based questions on Ka determination are frequently tested, along with applications of the blood buffer system in biological contexts. Once you have mastered this topic, you are ready to move on to further organic chemistry and analytical techniques in the rest of Unit 4, or transition to Unit 5 transition metal chemistry.

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